| 摘要: |
| We consider how small delays affect the integral-input-to-state stability (iiss) property for a system. Our result is similar to
the input-to-state stability (iss) result obtained in [1]: the iiss property will be preserved in a practical and semi-global manner
if the delay interval is small enough. However, since the iiss quantifies the robust stability in terms of a generalized L1 norm
of the inputs instead of a generalized L∞ norm of the inputs for the iss case, the techniques and proofs for the iss case do
not apply to the iiss case directly. While the proofs in [1] are based on the Lyapunov-Razumikhin approach, our proofs are
based on the iiss-Lyapunov functions for the zero-delay system. In addition to the interest by its own in showing how the iiss
property is affected by small delays, the result also serves to the study of the iiss property for singularly perturbed systems. |
| 关键词: Integral-input-to-state stability · Nonlinear systems · Small delays · Lyapunov method |
| DOI：https://doi.org/10.1007/s11768-023-00184-5 |
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| 基金项目: |
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| Integral input-to-state stability of systems with small delays |
| R. H. Harsha Nawarathna1,Yuandan Lin1,Yuan Wang1 |
| (1 Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL 33431, USA) |
| Abstract: |
| We consider how small delays affect the integral-input-to-state stability (iiss) property for a system. Our result is similar to
the input-to-state stability (iss) result obtained in [1]: the iiss property will be preserved in a practical and semi-global manner
if the delay interval is small enough. However, since the iiss quantifies the robust stability in terms of a generalized L1 norm
of the inputs instead of a generalized L∞ norm of the inputs for the iss case, the techniques and proofs for the iss case do
not apply to the iiss case directly. While the proofs in [1] are based on the Lyapunov-Razumikhin approach, our proofs are
based on the iiss-Lyapunov functions for the zero-delay system. In addition to the interest by its own in showing how the iiss
property is affected by small delays, the result also serves to the study of the iiss property for singularly perturbed systems. |
| Key words: Integral-input-to-state stability · Nonlinear systems · Small delays · Lyapunov method |
